# Math Help - Find Domain

1. ## Solve equations

1. Give the range of the function y = tan^-1 x

2. Give the value of tan^-1 5

2. Originally Posted by Kiwigirl

1. Give the range of the function y = tan^-1 x
There are two ways to do this problem. One way is the cowardly way they teach in school using a graph in that case look below to see that the range is,
$y\in (-\pi/2,\pi/2)$

The second way. The function $\tan^{-1}(x)$ is defined as the inverse function of the function,
$\tan x \mbox{ on } -\pi/2. Now there is a rule that the range of the inverse function is the domain of the orignal function. Since the domain of the original function is $(-\pi/2,\pi/2)$ thus the range of $\tan^{-1}(x)$ is $(-\pi/2,\pi/2)$

There is actually a third way (much more advanced). Find all such $y$ such as the equation $y=\tan^{-1}(x)$ has a solution.